Should I make my kid keep going with their business?

Two different questions get asked in the same sentence here, and separating them settles most of it.

The first is whether your kid should have to finish what they promised. Yes. Somebody is expecting them on Saturday, and a person who is expecting you is a real obligation regardless of how anyone feels about it that morning. That is enforceable, it is worth enforcing, and it is one of the better things this whole exercise teaches.

The second is whether they should keep going indefinitely because you think it is good for them. That one does not work, and the failure is not obvious for a while. A kid pushed through months of something they have internally quit learns a lesson, just not the one intended: having an idea leads to being trapped in it. The next time they want to start something, that memory is sitting there.

What you are protecting is not this business. It is their appetite for starting the next one, and that is a finite resource you can spend without noticing.

Before treating it as an ending, check whether it is a bad week. Two people said no, it rained, a friend was unimpressed, and everything feels flat. That is a hard stretch and not a verdict. Food, a break, and a next step small enough to feel possible resolves more of these than any conversation about commitment.

There is a middle option that almost nobody uses. Pause with a date. Stop for six weeks, tell the customers it is a break rather than a closure, and revisit in the middle of October. A real pause keeps the door open in a way that grinding does not, and it is what most adults would do with a side business that had gone stale.

If it is genuinely over, let them close it properly. Finish what was promised, tell each customer directly, and count what they made. A kid who can end something cleanly has learned something most adults handle badly, and they will start another one. A kid who was made to grind out something they had already quit usually does not.